Permutations and Combinations-Quiz-16

Permutations and Combinations Quiz-16

Dear Readers,

Permutations and Combinations is one of the most important chapters of Algebra in the JEE syllabus and other engineering exams. For JEE Mains, it has 4% weightage and for JEE Advanced, it has 5% weightage..

This section contain(s) 5 questions numbered 1 to 5. Each question contains statement 1(Assertion) and statement 2(Reason). Each question has the 4 choices (a), (b), (c) and (d) out of which only one is correct.

a)Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
b)Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
c)Statement 1 is True, Statement 2 is False
d)Statement 1 is False, Statement 2 is True
.

Q1. Statement 1: From a group of 8 men and 4 women at team of 5, including at least one women can be formed in 736 ways Statement 2: Number of ways of selecting at least one woman from 𝑚 men and 𝑛 women is ^𝑚+𝑛𝐶_𝑛 − ^𝑚𝐶_𝑛

•  (a)
•  (b)
•  (c)
•  (d)

Solution

Q2.Statement 1: If 𝑎,𝑏,𝑐 are positive integers such that 𝑎 + 𝑏 + 𝑐 ≤ 8, then the number of possible values of the ordered triplets (𝑎,𝑏,𝑐) is 56 Statement 2: The number of ways in which 𝑛 identical things can be distributed into 𝑟 different groups is ^𝑛−1𝐶_𝑟−1

•  (a)
•  (b)
•  (c)
•  (d)

Solution

Q3.  Statement 1: The number of ways in which three distinct numbers can be selected from the set {3¹,3²,3³,…,3¹⁰⁰,3¹⁰¹} so that they form a G.P. is 2500 Statement 2: If 𝑎,𝑏,𝑐 are in A.P., then 3^𝑎,3^𝑏,3^𝑐 are in G.P.

•  (a)
•  (b)
•  (c)
•  (d)

Solution

Q4. Statement 1: The number of ways of writing 1400 as a product of two positive integers is 12 Statement 2: 1400 is divisible by exactly three prime factors

•  (a)
•  (b)
•  (c)
•  (d)

Solution

Q5. Statement 1: Product of five consecutive natural numbers is divisible by 4! Statement 2: Product of 𝑛 consecutive natural numbers is divisible by (𝑛+1)!

•  (a)
•  (b)
•  (c)
•  (d)

Solution

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